Long Range Forces from Quantum Field Theory at Zero and Finite Temperature

Abstract

We discuss the derivation of Newtonian potentials in the framework of quantum field theory. We focus on two particular points: on long range forces i.e. forces which fall off as $1/r^n$ being mediated by light quanta like neutrinos or Goldstone bosons and on possible temperature dependence of such forces arising in situations when the exchanged quanta are in a thermal heat bath. Examples of the latter are cosmic relic photons and relic neutrinos. Among other things, we will show that the existence of cosmic relic neutrinos modifies the long tail of the two-neutrino exchange Feinberg-Sucher force drastically. Results concerning the potential mediated by two Goldstone bosons are also presented.